OK, I'm going to call the G# minor chord at the beginning a tonic chord. Then, obviously, there's quickly a modulating passage and we have a perfect authentic cadence at the end of the intro and the beginning of the first verse and we're in A major.

The G major chord works as a bVII, but how to explain the G minor? I think it suggests that D has been tonicized. I think it's a borrowed four chord in D.

Obviously, then, we have a perfect authentic cadence in F at the beginning of the third line. This time, I think the D is a V/ii chord.

If that's so, the next line is a sequence down a whole step in the key of Eb. (It just goes to the IV chord instead of the ii.) The chromatic movement at the end gets us back to the beginning for verse number two.

This verse is the same until the extension at the end. Maybe it's best to say that the whole extension, the last two lines, is basically in B major? It rests on F#, though, at the end of the first line. The D at the end would be a bIII, but ends up being a bVII instead when E is tonicized in the bridge.

That's a I-bVI-bVII-IV progression that repeats four times at the beginning, and the first time that this song has held on to any key center at all. Then, you have the repeat of the chords that make up the second part of the verse, in F and in Eb, plus the chromatic movement back to A for verse number three.

Verse three is the same as the second, but without the extension. What it does instead is move parallel from the Ab major chord to the G# minor 9th chord heard originally in the intro. This becomes the outro, then, moving from G# minor to the same E major seventh chord from the intro and ending there. I'll hold with calling this the key of G# minor even though it doesn't end on that chord.

So, in all, that makes for a total of seven different key centers (G# minor, A major, D major, F major, Eb major, B major, E major) that this song manages to traverse in its three minutes and eighteen seconds and its fifteen chords.